### Investigation of Data Locality and Fairness in MapReduce

```Investigation of Data Locality and
Fairness in MapReduce
Zhenhua Guo, Geoffrey Fox, Mo Zhou
Outline
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Introduction
Data Locality and Fairness
Experiments
Conclusions
MapReduce Execution Overview
Input file
block 0 1
2
Data locality
Stored locally
Shuffle between map
Stored in GFS
3
HDFS
Name node
Replication mgmt.
Block placement
Fault tolerance
……
oop
Operating System
MapReduce
Job tracker
oop
……
Storage: HDFS
- Files are split into blocks.
- Each block has replicas.
- All blocks are managed
by central name node.
Compute: MapReduce
- Each node has map
and reduce slots
- Tasks are scheduled to
- # of tasks <= # of slots
Operating System
Worker node 1
4
Worker node N
data block
Data Locality
“Distance” between compute and data
Different levels: node-level, rack-level, etc.
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The tasks that achieve node-level DL are called data local tasks
For data-intensive computing, data locality is important
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Energy consumption
Network traffic
Research goals
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Analyze state-of-the-art scheduling algorithms in MapReduce
Propose a scheduling algorithm achieving optimal data locality
Integrate Fairness
Mainly theoretical study
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5
Outline
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Introduction
Data Locality and Fairness
Experiments
Conclusions
Data Locality – Factors and Metrics
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Important factors
Symbol
Description
N
the number of nodes
S
the number of map slots on each node
I
the ratio of idle slots
T
the number of tasks to execute
C
replication factor
Metrics
the goodness of data locality
the percent of data local tasks (0% – 100%)
data locality cost
the data movement cost of job execution
The two metrics are not directly related.
 The goodness of data locality is good ⇏ Data locality cost is low
 The number of non data local tasks ⇎ The incurred data locality cost
Depends on scheduling strategy, dist. of input, resource availability, etc.
Non-optimality of default Hadoop sched.
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Problem: given a set of tasks and a set of idle slots, assign tasks to idle slots
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Consider one idle slot each time
Given an idle slot, schedule the task that yields the “best” data locality
Favor data locality
Achieve local optimum; global optimum is not guaranteed
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Each task is scheduled without considering its impact on other tasks
T1
T2
T3
Data block
schedule
Map slot. If its
color is black, the
slot is not idle.
......
Node A
T1
Node B
T2
Node C
(a) Instant system state
T3
Node A
Node B
Node C
(b) dl-shed scheduling
T3
T2
T1
Node A
Node B
Node C
(c) Optimal scheduling
Optimal Data Locality
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All idle slots need to be considered at once to achieve
global optimum
We propose an algorithm lsap-sched which yields optimal
data locality
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Reformulate the problem
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Use a cost matrix to capture data locality information
Find a similar mathematical problem: Linear Sum Assignment
Problem (LSAP)
Convert the scheduling problem to LSAP (not directly
mapped)
Prove the optimality
Optimal Data Locality – Reformulation
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m idle map slots {s1,…sm} and n tasks {T1,…Tn}
Construct a cost matrix C
s1
Cell Ci,j is the assignment cost if task Ti is T1 1
T2 0
assigned to idle slot sj
0: if compute and data are co-located … …
Tn-1 0
1: otherwise (uniform net. bw)
Tn 1
Reflects data locality
Represent task assignment with a function Φ
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s2
… sm-1 sm
1
…
0
0
1
…
0
1
…
…
…
…
1
…
0
0
0
…
0
1
Given task i, Φ(i) is the slot where it is assigned
T
C
Cost sum: Csum ( ) 
i 1 i (i )

Find an assignment to minimize Csum
g  min C sum ( )
lsap-uniform-sched
Optimal Data Locality – Reformulation
(cont.)
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Refinement: use real network bandwidth to calculate cost
Cell Ci,j is the incurred cost if task Ti is assigned to idle
slot sj
0: if compute and data are co-located
DS (Ti )
: otherwise
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max BW ( ND(Ti , c), N ( IS j ))
1i  Ri
s1
s2
… sm-1 sm
T1
1
3
…
0
0
T2
0
2
…
0
2.5
… … …
…
…
…
0.7 …
0
0
…
0
3
Tn-1 0
Tn 1.5
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0
Network Weather Service (NWS) can be used for network monitoring and
prediction
lsap-sched
Optimal Data Locality – LSAP
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LSAP: matrix C must be square
When a cost matrix C is not square, cannot apply LSAP
Solution 1: shrink C to a square matrix by removing rows/columns 
Solution 2: expand C to a square matrix 
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If n < m, create m-n dummy tasks, and use constant cost 0
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Apply LSAP, and filter out the assignment of dummy tasks
If n > m, create n-m dummy slots, and use constant cost 0
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Apply LSAP, and filter our the tasks assigned to dummy slots
s1
dummy
s2
… sm-1 sm
s1
…
sm sm+1 …
sn
T1
1.2 2.6
0
T1
1.8 …
0
0
…
0
…
… … … … …
…
…
…
…
…
…
…
Tn
0
2
3
0
0
Ti
0
… 2.3
0
…
0
Tn+1
0
0
0
0
0
0
0
Ti+1 1.3 …
3
0
…
0
…
… … … … …
…
…
…
…
…
…
…
Tm
0
Tn
4
…
0
0
…
0
0
0
(a) n < m
0
0
(b) n > m
dummy slots
Optimal Data Locality – Proof
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Do our transformations preserve optimality? Yes!
Assume LSAP algorithms give optimal assignments (for square matrices)
Proof sketch (by contradiction):
1)
2)
3)
4)
The assignment function found by lsap-sched is φ-lsap. Its cost sum is
Csum(φ-lsap)
The total assignment cost of the solution given by LSAP algorithms for the
expanded square matrix is Csum(φ-lsap) as well
The key point is that the total assignment cost of dummy tasks is |n-m| no
matter where they are assigned.
Assume that φ-lsap is not optimal.
Another function φ-opt gives smaller assignment cost.
Csum(φ-opt) < Csum(φ-lsap).
We extend function φ-opt, cost sum is Csum(φ-opt) for expanded square matrix
Csum(φ-opt) < Csum(φ-lsap)
⇨ The solution given by LSAP algorithm is not optimal.
⇨ This contradicts our assumption
Integration of Fairness
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Data locality and fairness conflict sometimes
Assignment Cost = Data Locality Cost (DLC) +
Fairness Cost (FC)
Group model
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Jobs are put into groups denoted by G.
Each group is assigned a ration w (the expected share of resource usage)
Real usage share:
(rti: # of running tasks of group i)
Group Fairness Cost:
Slots to allocate:
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(AS: # of all slots)
Approach 1: task FC  GFC of the group it belongs to
 Issue: oscillation of actual resource usage (all or none are
scheduled)
 A group i)slightly underuses its ration ii) has many waiting tasks
 drastic overuse of resources
Integration of Fairness (cont.)
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Approach 2: For group Gi,
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the FC of stoi tasks are set to GFCi,
the FC of other tasks are set to a larger value
Configurable DLC and FC weights to control the tradeoff
Assignment Cost = α· DLC + ϐ· FC
Outline
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Introduction
Data Locality and Fairness
Experiments (Simulations)
Conclusions
Experiments – Overhead of LSAP Solver
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Goal: to measure the time needed to solve LSAP
Hungarian algorithm (O(n3)): absolute optimality is
guaranteed
Matrix Size
Time
100 x 100
7ms
500 x 500
130ms
1700 x 1700
450ms
2900 x 2900
1s
Appropriate for small- and medium-sized clusters
Alternative: use heuristics to sacrifice absolute optimality
in favor of low compute time
Experiment – Background Recap
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Scheduling Algorithm
Description
dl-sched
Default Hadoop scheduling algorithm
lsap-uniform-sched
Our proposed LSAP-based algorithm
(Pairwise bandwidth is identical)
lsap-sched
Our proposed LSAP-based algorithm
(is network topology aware)
Metric
Description
the goodness of data locality
the percent of data local tasks (0% – 100%)
data locality cost
The data movement cost of job execution
9 data-local tasks, 1 non data local task with data movement cost 5
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The goodness of data locality is 90% (9 / 10)
Data locality cost is 5
Experiment – The goodness of data locality
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Measure the ratio of data-local tasks (0% – 100%)
# of nodes is from 100 to 500 (step size 50).
Each node has 4 slots. Replication factor is 3. The ratio of
idle slots is 50%.
better
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lsap-sched consistently improves the goodness of DL by 12% -14%
Experiment – The goodness of data locality
(cont.)
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Measure the ratio of data-local tasks (0% – 100%)
# of nodes is 100
better
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Increase replication factor ⇒ better data locality
More tasks ⇒ More workload ⇒ Worse data locality
lsap-sched outperforms dl-sched
Experiment – Data Locality Cost
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With uniform network bandwidth
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lsap-sched and lsap-uniform-sched become equivalent
better
better
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lsap-uniform-sched outperforms dl-sched by 70% – 90%
Experiment – Data Locality Cost (cont.)
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Hierarchical network topology setup
50% idle slots
better
better
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Introduction of network topology does not degrade performance substantially.
 dl-sched, lsap-sched, and lsap-uniform-sched are rack aware
lsap-sched outperforms dl-sched by up to 95%
lsap-sched outperforms lsap-uniform-sched by up to 65%
Experiment – Data Locality Cost (cont.)
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Hierarchical network topology setup
20% idle slots
better
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lsap-sched outperforms dl-sched by 60% - 70%
lsap-sched outperforms lsap-uniform-sched by 40% - 50%
With less idle capacity, the superiority of our algorithms decreases.
better
Experiment – Data Locality Cost (cont.)
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# of nodes is 100, vary replication factor
better
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Increasing replication factor reduces data locality cost.
lsap-sched and lsap-uniform-sched have faster DLC decrease
Replication factor is 3  lsap-sched outperforms dl-sched by over 50%
better
Experiment – Tradeoff between Data
Locality and Fairness
Fairness distance:
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Average:
Increase the weight of data locality cost
Conclusions
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Hadoop scheduling favors data locality
Hadoop scheduling is not optimal
We propose a new algorithm yielding optimal data
locality
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Uniform network bandwidth
Hierarchical network topology
Integrate fairness by tuning cost
Conducted experiments to demonstrate the effectiveness
More practical evaluation is part of future work
Questions?
Backup slides
MapReduce Model
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Input & Output: a set of key/value pairs
Two primitive operations
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Each map operation processes one input key/value pair and produces a set
of key/value pairs
Each reduce operation
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Merges all intermediate values (produced by map ops) for a particular key
Produce final key/value pairs
Operations are organized into tasks
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map: (k1,v1)
 list(k2,v2)
reduce: (k2,list(v2))  list(k3,v3)
Map tasks: apply map operation to a set of key/value pairs
Reduce tasks: apply reduce operation to intermediate key/value pairs
Each MapReduce job comprises a set of map and reduce (optional) tasks.
Use Google File System to store data
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Optimized for large files and write-once-read-many access patterns
HDFS is an open source implementation
```